1 static char help[] = "Model Equations for Advection-Diffusion\n";
2
3 /*
4 Page 9, Section 1.2 Model Equations for Advection-Diffusion
5
6 u_t = a u_x + d u_xx
7
8 The initial conditions used here different then in the book.
9
10 */
11
12 /*
13 Helpful runtime linear solver options:
14 -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view (geometric multigrid with three levels)
15
16 */
17
18 /*
19 Include "petscts.h" so that we can use TS solvers. Note that this file
20 automatically includes:
21 petscsys.h - base PETSc routines petscvec.h - vectors
22 petscmat.h - matrices
23 petscis.h - index sets petscksp.h - Krylov subspace methods
24 petscviewer.h - viewers petscpc.h - preconditioners
25 petscksp.h - linear solvers petscsnes.h - nonlinear solvers
26 */
27
28 #include <petscts.h>
29 #include <petscdm.h>
30 #include <petscdmda.h>
31
32 /*
33 User-defined application context - contains data needed by the
34 application-provided call-back routines.
35 */
36 typedef struct {
37 PetscScalar a, d; /* advection and diffusion strength */
38 PetscBool upwind;
39 } AppCtx;
40
41 /*
42 User-defined routines
43 */
44 extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *);
45 extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *);
46 extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *);
47
main(int argc,char ** argv)48 int main(int argc, char **argv)
49 {
50 AppCtx appctx; /* user-defined application context */
51 TS ts; /* timestepping context */
52 Vec U; /* approximate solution vector */
53 PetscReal dt;
54 DM da;
55 PetscInt M;
56
57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58 Initialize program and set problem parameters
59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60
61 PetscFunctionBeginUser;
62 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
63 appctx.a = 1.0;
64 appctx.d = 0.0;
65 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL));
66 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL));
67 appctx.upwind = PETSC_TRUE;
68 PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL));
69
70 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da));
71 PetscCall(DMSetFromOptions(da));
72 PetscCall(DMSetUp(da));
73 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
74 Create vector data structures
75 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
76
77 /*
78 Create vector data structures for approximate and exact solutions
79 */
80 PetscCall(DMCreateGlobalVector(da, &U));
81
82 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83 Create timestepping solver context
84 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85
86 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
87 PetscCall(TSSetDM(ts, da));
88
89 /*
90 For linear problems with a time-dependent f(U,t) in the equation
91 u_t = f(u,t), the user provides the discretized right-hand side
92 as a time-dependent matrix.
93 */
94 PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx));
95 PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx));
96 PetscCall(TSSetSolutionFunction(ts, (PetscErrorCode (*)(TS, PetscReal, Vec, void *))Solution, &appctx));
97
98 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99 Customize timestepping solver:
100 - Set timestepping duration info
101 Then set runtime options, which can override these defaults.
102 For example,
103 -ts_max_steps <maxsteps> -ts_max_time <maxtime>
104 to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
105 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106
107 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
108 dt = .48 / (M * M);
109 PetscCall(TSSetTimeStep(ts, dt));
110 PetscCall(TSSetMaxSteps(ts, 1000));
111 PetscCall(TSSetMaxTime(ts, 100.0));
112 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
113 PetscCall(TSSetType(ts, TSARKIMEX));
114 PetscCall(TSSetFromOptions(ts));
115
116 /*
117 Evaluate initial conditions
118 */
119 PetscCall(InitialConditions(ts, U, &appctx));
120
121 /*
122 Run the timestepping solver
123 */
124 PetscCall(TSSolve(ts, U));
125
126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127 Free work space. All PETSc objects should be destroyed when they
128 are no longer needed.
129 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130
131 PetscCall(TSDestroy(&ts));
132 PetscCall(VecDestroy(&U));
133 PetscCall(DMDestroy(&da));
134
135 /*
136 Always call PetscFinalize() before exiting a program. This routine
137 - finalizes the PETSc libraries as well as MPI
138 - provides summary and diagnostic information if certain runtime
139 options are chosen (e.g., -log_view).
140 */
141 PetscCall(PetscFinalize());
142 return 0;
143 }
144 /* --------------------------------------------------------------------- */
145 /*
146 InitialConditions - Computes the solution at the initial time.
147
148 Input Parameter:
149 u - uninitialized solution vector (global)
150 appctx - user-defined application context
151
152 Output Parameter:
153 u - vector with solution at initial time (global)
154 */
InitialConditions(TS ts,Vec U,AppCtx * appctx)155 PetscErrorCode InitialConditions(TS ts, Vec U, AppCtx *appctx)
156 {
157 PetscScalar *u, h;
158 PetscInt i, mstart, mend, xm, M;
159 DM da;
160
161 PetscFunctionBeginUser;
162 PetscCall(TSGetDM(ts, &da));
163 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
164 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
165 h = 1.0 / M;
166 mend = mstart + xm;
167 /*
168 Get a pointer to vector data.
169 - For default PETSc vectors, VecGetArray() returns a pointer to
170 the data array. Otherwise, the routine is implementation dependent.
171 - You MUST call VecRestoreArray() when you no longer need access to
172 the array.
173 - Note that the Fortran interface to VecGetArray() differs from the
174 C version. See the users manual for details.
175 */
176 PetscCall(DMDAVecGetArray(da, U, &u));
177
178 /*
179 We initialize the solution array by simply writing the solution
180 directly into the array locations. Alternatively, we could use
181 VecSetValues() or VecSetValuesLocal().
182 */
183 for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h);
184
185 /*
186 Restore vector
187 */
188 PetscCall(DMDAVecRestoreArray(da, U, &u));
189 PetscFunctionReturn(PETSC_SUCCESS);
190 }
191 /* --------------------------------------------------------------------- */
192 /*
193 Solution - Computes the exact solution at a given time.
194
195 Input Parameters:
196 t - current time
197 solution - vector in which exact solution will be computed
198 appctx - user-defined application context
199
200 Output Parameter:
201 solution - vector with the newly computed exact solution
202 */
Solution(TS ts,PetscReal t,Vec U,AppCtx * appctx)203 PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx)
204 {
205 PetscScalar *u, ex1, ex2, sc1, sc2, h;
206 PetscInt i, mstart, mend, xm, M;
207 DM da;
208
209 PetscFunctionBeginUser;
210 PetscCall(TSGetDM(ts, &da));
211 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
212 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
213 h = 1.0 / M;
214 mend = mstart + xm;
215 /*
216 Get a pointer to vector data.
217 */
218 PetscCall(DMDAVecGetArray(da, U, &u));
219
220 /*
221 Simply write the solution directly into the array locations.
222 Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
223 */
224 ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t);
225 ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t);
226 sc1 = PETSC_PI * 6. * h;
227 sc2 = PETSC_PI * 2. * h;
228 for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(sc1 * (PetscReal)i + appctx->a * PETSC_PI * 6. * t) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i + appctx->a * PETSC_PI * 2. * t) * ex2;
229
230 /*
231 Restore vector
232 */
233 PetscCall(DMDAVecRestoreArray(da, U, &u));
234 PetscFunctionReturn(PETSC_SUCCESS);
235 }
236
237 /* --------------------------------------------------------------------- */
238 /*
239 RHSMatrixHeat - User-provided routine to compute the right-hand-side
240 matrix for the heat equation.
241
242 Input Parameters:
243 ts - the TS context
244 t - current time
245 global_in - global input vector
246 dummy - optional user-defined context, as set by TSetRHSJacobian()
247
248 Output Parameters:
249 AA - Jacobian matrix
250 BB - optionally different matrix used to construct the preconditioner
251
252 Notes:
253 Recall that MatSetValues() uses 0-based row and column numbers
254 in Fortran as well as in C.
255 */
RHSMatrixHeat(TS ts,PetscReal t,Vec U,Mat AA,Mat BB,PetscCtx ctx)256 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec U, Mat AA, Mat BB, PetscCtx ctx)
257 {
258 Mat A = AA; /* Jacobian matrix */
259 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */
260 PetscInt mstart, mend;
261 PetscInt i, idx[3], M, xm;
262 PetscScalar v[3], h;
263 DM da;
264
265 PetscFunctionBeginUser;
266 PetscCall(TSGetDM(ts, &da));
267 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
268 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
269 h = 1.0 / M;
270 mend = mstart + xm;
271 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272 Compute entries for the locally owned part of the matrix
273 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
274 /*
275 Set matrix rows corresponding to boundary data
276 */
277
278 /* diffusion */
279 v[0] = appctx->d / (h * h);
280 v[1] = -2.0 * appctx->d / (h * h);
281 v[2] = appctx->d / (h * h);
282 if (!mstart) {
283 idx[0] = M - 1;
284 idx[1] = 0;
285 idx[2] = 1;
286 PetscCall(MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES));
287 mstart++;
288 }
289
290 if (mend == M) {
291 mend--;
292 idx[0] = M - 2;
293 idx[1] = M - 1;
294 idx[2] = 0;
295 PetscCall(MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES));
296 }
297
298 /*
299 Set matrix rows corresponding to interior data. We construct the
300 matrix one row at a time.
301 */
302 for (i = mstart; i < mend; i++) {
303 idx[0] = i - 1;
304 idx[1] = i;
305 idx[2] = i + 1;
306 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES));
307 }
308 PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY));
309 PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY));
310
311 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0));
312 mend = mstart + xm;
313 if (!appctx->upwind) {
314 /* advection -- centered differencing */
315 v[0] = -.5 * appctx->a / (h);
316 v[1] = .5 * appctx->a / (h);
317 if (!mstart) {
318 idx[0] = M - 1;
319 idx[1] = 1;
320 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES));
321 mstart++;
322 }
323
324 if (mend == M) {
325 mend--;
326 idx[0] = M - 2;
327 idx[1] = 0;
328 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES));
329 }
330
331 for (i = mstart; i < mend; i++) {
332 idx[0] = i - 1;
333 idx[1] = i + 1;
334 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES));
335 }
336 } else {
337 /* advection -- upwinding */
338 v[0] = -appctx->a / (h);
339 v[1] = appctx->a / (h);
340 if (!mstart) {
341 idx[0] = 0;
342 idx[1] = 1;
343 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES));
344 mstart++;
345 }
346
347 if (mend == M) {
348 mend--;
349 idx[0] = M - 1;
350 idx[1] = 0;
351 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES));
352 }
353
354 for (i = mstart; i < mend; i++) {
355 idx[0] = i;
356 idx[1] = i + 1;
357 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES));
358 }
359 }
360
361 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
362 Complete the matrix assembly process and set some options
363 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
364 /*
365 Assemble matrix, using the 2-step process:
366 MatAssemblyBegin(), MatAssemblyEnd()
367 Computations can be done while messages are in transition
368 by placing code between these two statements.
369 */
370 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
371 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
372
373 /*
374 Set and option to indicate that we will never add a new nonzero location
375 to the matrix. If we do, it will generate an error.
376 */
377 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
378 PetscFunctionReturn(PETSC_SUCCESS);
379 }
380
381 /*TEST
382
383 test:
384 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
385 requires: double
386 filter: grep -v "total number of"
387
388 test:
389 suffix: 2
390 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
391 requires: x
392 output_file: output/ex3_1.out
393 requires: double
394 filter: grep -v "total number of"
395
396 TEST*/
397